If `A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]]` then show that A`A^(T)=A^(T)A=I`

A=[[Cos alpha,sin alpha],[-Sin alpha,cos alpha]] then A^(2)

If A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then verify that A'A=I

A=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] , then find | A |

If A=[cos alpha sin alpha-sin alpha cos alpha], then verify that A^(T)A=I_(2)

If A_(alpha)=[[cos alpha,sin alpha-sin alpha,cos alpha]]. Prove that

If A,=[[cos alpha,sin alpha-sin alpha,cos alpha]] then show that ,A^(2)=[[cos2 alpha,sin2 alpha-sin2 alpha,cos2 alpha]]

If A,=[[cos alpha,sin alpha-sin alpha,cos alpha]] is such that A^(T),=A^(-1), find alpha

If A(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then A(alpha)A(beta)